The England international completed a medical on Wednesday night at the national team's training ground in Burton-on-Trent and agreed a five-year contract worth a reported £120,000-a-week.
Oxlade-Chamberlain rejected the chance to sign for reigning Premier League champions Chelsea on higher terms than those on offer at Anfield, also rejecting a £180,000-a-week contract offer from Arsenal.
The 24-year-old was concerned about the game-time he would receive in his preferred central midfield position for Arsenal and the Blues but believes he can cement a starting spot there under Jürgen Klopp.
The Gunners had said they would not do business with Liverpool due to strained relations between the two clubs and because they perceive the Merseyside outfit as closer rivals than Chelsea, but conceded defeat after Oxlade-Chamberlain turned down a £40 million move to Antonio Conte's side.
That was enough to force the North London outfit - unwilling to let the former Southampton youngster leave on a free next summer - to change their stance despite Arsène Wenger's recent claims that they would hold Oxlade-Chamberlain to the remainder of his contract and let him leave on for nothing in 12 months' time.
Midfielder moves to Merseyside in search of more minutes
Oxlade-Chamberlain's deal ran out next summer and he rejected several offers to improve and extend his terms at Arsenal as he looked for more consistent first-team football, which he believes he has found on Merseyside.
Oxlade-Chamberlain becomes Liverpool's fifth signing of the summer after Dominic Solanke, Mohamed Salah, Andrew Robertson and Naby Keïta - who will join the club from RB Leipzig in a club-record deal in July 2018.
Before the window closes at 11pm tonight, Liverpool could still seal deals for Southampton centre-back Virgil van Dijk and AS Monaco attacking midfielder Thomas Lemar if they can convince their clubs into selling.
Oxlade-Chamberlain made 198 appearances for Arsenal after a £12 million move from Southampton six years ago and scored 20 goals during his spell at the Emirates Stadium.
In 45 appearances in all competitions last term, the Reds' new No.21 provided 11 assists and six goals for Arsenal. He had started all four of their games this season, including Sunday's 4-0 defeat at Anfield, when he played for just over an hour as a left-wing-back.